Having watched the series in Machete Order (IV-V-II-III-VI), I want to argue that III is improved when watched in conjunction with II as a two-part flashback (I still like EI though).
I'd say that when you watch those as a two-part film, and not just the middle and end of a prequel trilogy, Anakin's fall becomes a master course in how to write a heroic protagonist turning evil. Christensen clearly had a more consistent direction and inspiration in Anakin's fall then in almost any other category of Anakin's portrayal.
The biggest improvement to III when you watch it immediately after II is that we start the film knowing that Anakin's already deeply compromised by the Sand People Massacre. We don't have the distraction of the purely innocent 9 year old from EI, and Palpatine's reminder of the event in the Invisible Hand immediately exposes Anakin's sometimes overlooked personality trait: he knows that what he did was wrong, so he's spending III convinced that he's not a good Jedi, not really.
Which makes Palpatine's seduction that much more brilliant.
Now, Anakin isn't just compelled by his selfish attachment to Padme, he's also guilt driven enough to look for a way to justify or erase his sins, because he hasn't had to atone for them. So when Palpatine starts defaming the Jedi to him, Anakin isn't looking at the Order as his friends and as his faith, he's looking at them as a reflection of himself.
It puts a whole new spin on:
"The Sith think inwardly only of themselves."
"And the Jedi don't?"
With Anakin's massacre and subsequent confession and emotional breakdown so fresh in the audience's mind, we know that in that instant, Anakin is seeing a way to view the Order not as something he's unworthy of, but as something that allowed him to be the way he is. It's their failings, not his. It's the ultimate cynicism motivator. and now that we know we're already looking at a child killer who knew what he did was wrong, we see the younglings massacre as just him applying his new world view after feeling he's no better than the Jedi are, and they're no better then him.
It even makes his "It is...too late for me, my son," line in ROTJ more powerful. Anakin knows that he's evil, and he can never really escape his own guilt, even when drunk on the darkside.